Answer:
0.00000223
Explanation:
pKa for C2H5NH3+ = 10.7
pKw = 14.0
pKa + pKb = pKw
10.7 + pKb = 14.0
pKb = 14.0 - 10.7
pKb = 3.30
C2H5NH3Cl is a salt of ethylamine and HCl so it will dissolve in water to produce C2H5NH3^+ + Cl^-
The base hydrolysis reaction: C2H5NH3^+(aq) + H2O(l) <=> C2H5NH2(aq) + H3O^+(aq)
This reaction is described by Kb.
Kb = [C2H5NH2][H3O^+]/[C2H5NH3^+]
Let [C2H5NH2] = [H3O^+] = x,
so [C2H5NH3^+] = 0.26 - x
Kb = x^2/(0.26 - x) = 2.00 x 10^-11
Let's solve for x. In this equation, It is possible to solve without the use quadratic equation. So we can assume that 0.26 - x is approximately equal to 0.26. We won't know until we do the calculation.
We get: x^2 + 2.00 x 10^-11x - 4.99 x 10^-12 = 0
With the use of a quadratic calculator.
x = 2.23 x 10^-6 M = [C2H5NH2] = [H3O^+]
0.26 - x is just 0.26 M in this problem because 2.23 x 10^-6 M is insignificant.
[C2H5NH3^+] = 0.26 M = [Cl^-]
NOTE:
pH = -log [H3O^+] = -log(2.23 x 10^-6) = 5.65
Ka is the acid dissociation constant
Kb is the base dissociation constant
